Elijah Lewis wants to set up a fund to pay for his daughter's education. In order to pay her tution and expenses, he will need $24,000 in four years, $25,800 in five years, $27,300 in six years, and $29,100 in seven years. If he can put money into a fund that pays 6 percent interest, what lump-sum payment must Elijah place in the fund today to meet his college funding goals? Round the answer to the nearest cent. Round PV-factor to three decimal places.

Elijah Lewis needs to determine how much to invest in a fund today that earns 6% interest in order to meet his daughter's college expenses for the next several years. To solve this problem, we will use the concept of the **present value** (PV) of a future amount, which discounts future cash flows to their present value using the formula:

\[
PV = \dfrac{FV}{(1 + r)^n}
\]

Where:
- $ PV $ is the present value (the amount needed today).
- $ FV $ is the future value (the payment required in the future).
- $ r $ is the interest rate per period (6% or 0.06 in this case).
- $ n $ is the number of periods (in years).

We'll calculate the present value of each future cash flow and sum them up to find the lump sum required today.

### Step-by-step calculation:

1. **Year 4**: $24,000
\[
PV = \dfrac{24,000}{(1 + 0.06)^4} = \dfrac{24,000}{(1.06)^4}
\]

2. **Year 5**: $25,800
\[
PV = \dfrac{25,800}{(1 + 0.06)^5} = \dfrac{25,800}{(1.06)^5}
\]

3. **Year 6**: $27,300
\[
PV = \dfrac{27,300}{(1 + 0.06)^6} = \dfrac{27,300}{(1.06)^6}
\]

4. **Year 7**: $29,100
\[
PV = \dfrac{29,100}{(1 + 0.06)^7} = \dfrac{29,100}{(1.06)^7}
\]

Now, I'll calculate the individual present values and sum them to get the lump sum Elijah needs to invest today.Elijah Lewis needs to invest **$76,888.09** today to meet his daughter's future college expenses.

Here are the present values of each future payment, rounded to the nearest cent:
1. Present value of $24,000 in 4 years: **$19,010.25**
2. Present value of $25,800 in 5 years: **$19,279.26**
3. Present value of $27,300 in 6 years: **$19,245.42**
4. Present value of $29,100 in 7 years: **$19,353.16**

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. How would the lump sum change if the interest rate was 5% instead of 6%?
2. What if the expenses were delayed by one year for each payment?
3. How much would Elijah need if his daughter requires an additional $10,000 in year 8?
4. What is the total amount paid in nominal terms without accounting for interest?
5. How would monthly contributions affect the total required?

**Tip:** Always account for the time value of money when planning for future payments!

Elijah Lewis wants to set up a fund to pay for his daughter's education. In order to pay her tuition and expenses, he will need $24,000 in four years, $25,800 in five years, $27,300 in six years, and $29,100 in seven years. If he can put money into a fund that pays 6 percent interest, what lump-sum payment must Elijah place in the fund today to meet his college funding goals? Round the answer to the nearest cent. Round PV-factor to three decimal places.

Learn how to calculate the lump-sum investment required today to cover future educational expenses using present value formulas and compound interest. This problem involves key financial concepts such as time value of money, interest rates, and future value calculations. Suitable for advanced high school or college students.

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